The present disclosure relates generally to intrusion detection systems, and particularly to radio detection and ranging (RADAR) intrusion detection systems.
There is a need for indoor security devices to monitor areas subject to penetration by trespassers and also to alert authorities when personnel have entered a hazardous zone. One commonly employed technique is that of electromagnetic RADAR. It is well known in the art that a RADAR system may be used to monitor an area even though there is no direct visible line of sight from the RADAR unit to the area under surveillance, as a RADAR signal may often successfully penetrate and return through common building materials, thereby allowing the RADAR unit to be hidden or inconspicuous.
Referring now to FIG. 1, a block schematic diagram of a basic signal processing operation is depicted. A baseline system 100 operates as a simple Pulsed Doppler radar using analog signal processing. A radio frequency (RF) pulse generator 105 produces a first burst and a second burst of microwave energy via an antenna 110, the bursts having a center frequency of 5.8 GHz (+/−75 MHz). As used herein, the term burst shall refer to a short duration portion of a sine wave of microwave energy. This frequency is part of the Industrial, Scientific, and Medical (ISM) band reserved for unlicensed use at limited transmit power levels. In the United States, three of the commonly used ISM bands occupy frequencies from 902-928 MHz, 2400-2483.5 MHz (also herein referred to as the 2.4 GHz band), and 5725-5850 MHz (also herein referred to the 5.8 GHz band). The two bursts are separated by some time interval from about 10 nanoseconds (ns) to about 80 ns, depending on the range of the region to be monitored, thereby defining the range to be monitored. In an embodiment, the duration of the bursts shall be less than the delay between the first and second burst. The burst pairs are generated at a rate of roughly 12 kHz. The first burst illuminates the target and the second burst (also herein referred to as a reference burst) is used to derive a Doppler signal. The RADAR unit 100 transmits the second burst in addition to the first, but the return of the second burst is ignored and has no effect on the processing. If it is desired that the RADAR not actually transmit the second burst, this can be accomplished through the use of a standard RADAR structure, where the reference burst is supplied to the receiver by a separate local oscillator and the antenna is switched back and forth between transmitter and receiver subsections by an analog switch. Such structures are described, for example, in RADAR Design Principles, by F. E. Nathanson (McGraw Hill, 1991).
In response to the reception of the reflection of the first transmitted burst at the antenna 110 it is, in effect, added to the second burst, and the sum is processed by a signal processing chain 115, starting with an envelope detector 120. The envelope detector 120 (also herein referred to as a non-linearity or a demodulator) may comprise one or more diodes in series followed by a low-pass filter (LPF) 130. For the duration of that period during which the reflected burst overlaps with the reference pulse, the amplitude of the envelope detector (also herein referred to as a demodulator) 120 output oscillates with a frequency equal to the difference of the frequency of the reference burst and the reflected first burst. If a target is moving at one foot/sec, the Doppler frequency is approximately 12 Hz when using a center frequency in the 5.8 GHz band, so that the output of the demodulator 120 will appear constant over the overlap period for normal walking speeds. The output of the demodulator 120 should be considered a sampled version of a continuous Doppler signal, so that the output of the demodulator 120 is a 12 kHz pulse sequence composed of a static part and a part oscillating at the Doppler frequency. The static part originates in the non-overlapped portions of the reflected and reference pulses and includes a constant part within the overlap interval that is due to the difference in amplitude between the return burst and the reference burst. The oscillating part originates in the pulse overlap region, as described below.
If the envelope detector 120 is considered to be a half-wave square law device and the associated low-pass filter 130 has a critical frequency low enough to block a signal of the form cos(2πf0+θ0), where f0 is the transmitted center frequency, and if the input is given by Equation-1:
                    input        =                  {                                                                      cos                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          0                                                ⁢                        t                                            +                                              θ                        0                                                              )                                                                                                                    for                    ⁢                                                                                  ⁢                    0                                    ≤                  t                  <                                                            T                      p                                        -                    Δ                                                                                                                                            cos                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            0                                                    ⁢                          t                                                +                                                  θ                          0                                                                    )                                                        +                                                            A                      1                                        ⁢                                          cos                      ⁡                                              (                                                                              2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                                                          f                              1                                                        ⁢                            t                                                    +                                                      θ                            1                                                                          )                                                                                                                                                                                    for                      ⁢                                                                                          ⁢                                              T                        p                                                              -                    Δ                                    ≤                  t                  <                                      T                    p                                                                                                                                            A                    1                                    ⁢                                      cos                    ⁡                                          (                                                                        2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            1                                                    ⁢                          t                                                +                                                  θ                          1                                                                    )                                                                                                                                        for                    ⁢                                                                                  ⁢                                          T                      p                                                        ≤                  t                  <                                                            2                      ⁢                                                                                          ⁢                                              T                        p                                                              -                    Δ                                                                                                          Equation        ⁢                                  ⁢        1            
where:
t is a variable representing continuous time;
θ0 is a random initial phase angle of the transmitted and reflected bursts;
A1 is the amplitude of the returned burst;
Tp is the pulse duration;
f1 is the Doppler-shifted center frequency of the radar return;
θ1 is the phase of the Doppler-shifted center frequency; and
Δ is the duration of the burst overlap.
The output of the envelope detector is approximated by Equation-2 to be:
                    ⁢          Equation      ⁢                          ⁢      2            output    =          {                                                  1              2                                                                          for                ⁢                                                                  ⁢                0                            ≤              t              <                                                T                  p                                -                Δ                                                                                                                          A                  1                                ⁢                                  cos                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                                                  π                          ⁡                                                      (                                                                                          f                                0                                                            -                                                              f                                1                                                                                      )                                                                          ⁢                        t                                            +                                              θ                        0                                            -                                              θ                        1                                                              )                                                              +                                                                                            for                  ⁢                                                                          ⁢                                      T                    p                                                  -                Δ                            ≤              t              <                              T                p                                                                                                        1                2                            ⁢                              (                                  1                  +                                      A                    1                    2                                                  )                                                                                                                                                                  A                1                2                            2                                                                          for                ⁢                                                                  ⁢                                  T                  p                                            ≤              t              <                                                2                  ⁢                                                                          ⁢                                      T                    p                                                  -                Δ                                                                          0                                              otherwise                                          since the nonlinearity 120 will produce sum and difference frequencies for every narrowband signal passing through it, and the low-pass filter 130 will pass only the difference frequencies. (Here it is assumed that the reference burst appears first; the order of the first and last segment will be reversed in Equation-2 if the radar return is first.)
Referring now to FIG. 2, a burst 150 of the kind represented by Equation-2 is depicted. A central, raised portion 155 of the burst 150 oscillates and another portion 160 is static from burst to burst. It will be appreciated that FIG. 2 depicts an unrealistically strong reflected first burst, (or an unrealistically weak reference burst). It is considered in general that the reference burst has unit amplitude, and the typical amplitude of the return will be much less. Contrary to this expectation, FIG. 2 assumes A1=1, showing that the return and reference have the same amplitude.
It will be appreciated that an amplitude of a signal at the output of an integrator 125 in FIG. 1 is proportional to the product of the duration of the burst overlap and the amplitude of the radar return (assuming unit amplitude reference burst). The “2-stage amp” low-pass filter 130 will convert the sequence of bursts 150, depicted in FIG. 2, coming from the envelope detector 120 into a continuous signal, and a high-pass filter 135 (also herein referred to as a DC block) will remove the portions of the output represented by Equation-2 that do not vary from burst to burst. Thus, the portion of the sequence of bursts represented by Equation-2 that contributes to the continuous signal at the output of the DC block may be approximated by Equation-3:
                              f          ⁡                      (            t            )                          =                              A            1                    ⁢                                                    ∑                ∞                                            k                =                ∞                                      ⁢                                          cos                ⁡                                  (                                                            2                      ⁢                                                                                          ⁢                                              π                        ⁡                                                  (                                                                                    f                              0                                                        -                                                          f                              1                                                                                )                                                                    ⁢                      kT                                        +                                          θ                      0                                        -                                          θ                      1                                                        )                                            ⁢                                                rect                  Δ                                ⁡                                  (                                      t                    -                    kT                                    )                                                                                        Equation        ⁢                                  ⁢        3            
where:
k is an index variable associated with the sequence of pulse pairs;
rectΔ is a rectangular time window of duration Δ;
Δ is the overlap duration; and
T is the pulse repetition time.
It will be appreciated that this is an approximation because the amplitude does not change at all over the overlap interval.
If M is the component of the velocity of the target in the direction of the radar, then the frequency of the return is given by
            f      1        =                  f        0            ⁡              (                  1          -                                    2              ⁢              M                        c                          )              ,so at
      (                  f        0            -              f        1              )    =                    2        ⁢        M            c        ⁢                  f        0            .      
The Fourier transform (FT) of f(t) is given by Equation-4:
                              F          ⁡                      (            ω            )                          =                              A            1                    ⁢                      ⅇ                          jω              ⁢                              Δ                2                                              ⁢                                    2              ⁢                              sin                ⁡                                  (                                      Δω                    2                                    )                                                      ω                    ⁢                                    ∑                              n                =                                  -                  ∞                                            ∞                        ⁢                                                  ⁢                          D              ⁡                              (                                  ω                  -                                      n                    T                                                  )                                                                        Equation        -        4            
where:
ω is the continuous radian frequency variable of the FT;
n is the index variable associated with the multiple frequency domain images of the Doppler spectrum; and
D(ω) is the FT of
      cos    ⁡          (                        2          ⁢          π          ⁢                                    2              ⁢              M                        c                    ⁢          t                +                  θ          0                -                  θ          1                    )        .
This is multiplied by the frequency response of the analog low-pass filter 130, H(ω), which suppresses all but the n=0 term:
                              G          ⁡                      (            ω            )                          =                                            H              ⁡                              (                ω                )                                      ⁢                          F              ⁡                              (                ω                )                                              ≅                                    A              1                        ⁢                          ⅇ                              jω                ⁢                                  Δ                  2                                                      ⁢                                          2                ⁢                                                                  ⁢                                  sin                  ⁡                                      (                                          Δω                      2                                        )                                                              ω                        ⁢                          D              ⁡                              (                ω                )                                                                        Equation        -        5            
Because the main lobe of the sinc function (sinc(t)=sin(πt)/πt) in Equation-5 is much wider than the Doppler signal spectrum, the output of the low pass filter 130 is approximately equal to the inverse Fourier transform of the Doppler spectrum times the peak value of sinc function:
                              g          ⁡                      (            t            )                          =                                            A              1                        ⁢                                                                            -                  1                                            ⁡                              [                                                      Δⅇ                                          jω                      ⁢                                              Δ                        2                                                                              ⁢                                      D                    ⁡                                          (                      ω                      )                                                                      ]                                              =                                    A              1                        ⁢            Δ            ⁢                                                  ⁢                          cos              ⁡                              (                                                      2                    ⁢                    π                    ⁢                                                                  2                        ⁢                        M                                            c                                        ⁢                                          (                                              t                        -                                                  Δ                          2                                                                    )                                                        +                                      θ                    0                                    -                                      θ                    1                                                  )                                                                        Equation        -        6            since the sinc function evaluated at zero is
                                                        2              ⁢                                                          ⁢                              sin                ⁡                                  (                                      Δω                    2                                    )                                                      ω                    ⁢                      ❘                          ω              =              0                                      =        Δ                            Equation        -        7            
Thus, the amplitude of this reconstructed continuous signal is proportional to Δ, the overlap duration, times the amplitude of the return, A1. If the center frequency of the Doppler signal is high enough (not too close to zero), the signal passes through the high-pass filter 135 (DC block), and the result is given by Equation-6. The analog Doppler signal at the output of the high-pass filter 135 is rectified by a full-wave rectifier 140 and the result is integrated to produce a Moving Target Indicator (MTI) signal, which is proportional to the amplitude of the Doppler signal. The time constant of this final integrator is important in that it determines a dwell time. The dwell time is that period which must elapse before the MTI signal fully responds to any change in range gate, pulse parameters or target motion. Simulations have used the dwell time of approximately 500 milliseconds. A signal 145 at the output of the integrator is compared to a threshold in the current system to detect the presence of a moving target.
The system described above is based on analog signal processing. At the input of the integrator 125, the signal-to-noise ratio must be great enough to allow detection. This means that the noise floor at that point must be lower than the signal level resulting from the maximum range and minimum range gate overlap for which detection is expected.
State of the art intrusion RADAR systems are capable to sense and respond to the motion of a target. As used herein, the word “target” shall refer to any moving object the radar system is capable to detect, with the understanding that the most common “targets” are likely to be people walking throughout the monitored area. Current indoor surveillance RADAR systems are limited to providing information relating only to the presence of motion within the monitored area. There is therefore a need to devise surveillance RADAR systems that can more effectively function in light of these shortcomings of the present systems in the art.